Often in the process matrix framework the term `causal' seems to refer simply to the transmission of information between systems, so for example the simplest kind of `causally ordered' processes are just one-way signalling processes - in effect \(A\)  is regarded as being a cause of \(B\)  if and only if \(p(B | A) \ne p(B)\)Some proponents of the process matrix formalism seem inclined to identify causation with signalling[1]}, but others take a more nuanced approach - for example, ref [2]} acknowledges that signalling is not a necessary condition for the presence of a causal relation, as one can imagine classical cases where two causal influences exactly cancel one another out, so there is no observable signalling effect even though there are cause-effect relations. Thus ref [2]} merely uses signalling as a sign that causation is present, rather than a definition of causation.. This information-theoretic way of thinking about causation is essentially a version of Lewis' simplest probabilistic counterfactual theory of causation[4]}, where we say that \(A\)  is a cause of \(B\)  if and only if, if \(A\)  had not occurred, the chance of \(B\)  occurring would be less than its actual chance. In the process framework we don't particularly care about whether \(A\)  makes \(B\)  more or less probable as long as it changes the probability of \(B\) , but it is clear that the approaches are similarly motivated and will have similar advantages and disadvantages. In particular, it is well-recognised[5]} that the simplest counterfactual account is not asymmetric and hence must rely on contingent external considerations (e.g. thermodynamics) if it is to recover the asymmetry of causation, and evidently the process matrix formulation faces a similar problem, since a relation defined in terms of the possibility of signalling between two variables is evidently not inherently asymmetric.
